Growth index in an accelerating universe

We obtain the exact analytic form of growth index (f = Ωm(a) ) at present epoch in a flat universe with including the constant equation of state of dark energy (ωde). For the cosmological constant (ωde = −1) we obtain γ = 0.5547 which is very close to the well known value 6/11. However, if ωde = −0.9, then γ gives rise to 0.6405. Ω 0 m dependence of γ is fairly small for the viable range of the current matter energy density 0.2 ≤ Ω0m ≤ 0.3. (0.6% and 3% changes in γ for ωde equal to −1 and −0.9, respectively.) The difference of peculiar velocity values from the different choices of γ is about 11% for Ω0m = 0.3. This simple but accurate formula which covers a large class of dark energy models will provide a practical tool for galaxy redshift survey to measure the matter density and the peculiar velocity. The background evolution equations in a flat Friedmann-RobertsonWalker universe (ρm + ρde = ρcr) are ( ȧ a )2 = 8πG 3 (ρm + ρde) = 8πG 3 ρcr , (1) 2 ä a + ( ȧ a )2 = −8πGωdeρde , (2) where ωde is the equation of state (eos) of dark energy, ρm and ρde are the energy densities of the matter and the dark energy, respectively. We consider the constant ωde only. The dark energy does not participate directly